https://file.aiquickdraw.com/mathbot/file/1726534130762zscgb0vj.jpg

Let's solve these two problems by ordering the numbers and verifying them.

### Problem 21:
You need to order the numbers: 
\[
1.84, \sqrt{5}, \frac{5}{2}, 2.3, \sqrt{3}
\]

1. **Convert to decimals**:
   - \( \sqrt{5} \approx 2.236 \)
   - \( \frac{5}{2} = 2.5 \)
   - \( \sqrt{3} \approx 1.732 \)

2. Now, we have:
   - \( 1.84 \)
   - \( \sqrt{5} \approx 2.236 \)
   - \( \frac{5}{2} = 2.5 \)
   - \( 2.3 \)
   - \( \sqrt{3} \approx 1.732 \)

3. **Order from least to greatest**:
   \[
   \sqrt{3} \approx 1.732, \ 1.84, \ \sqrt{5} \approx 2.236, \ 2.3, \ \frac{5}{2} = 2.5
   \]

### Problem 22:
You need to order the numbers:
\[
-3.01, -2.95, -2.9, -3.1, -3.5
\]

These numbers are already in decimal form. Let's sort them from least to greatest:
\[
-3.5, -3.1, -3.01, -2.95, -2.9
\]

### Verification by Graphing:
You can verify these by graphing them on a number line. On the first number line (for Problem 21), place the values corresponding to:
- \( \sqrt{3} \approx 1.732 \)
- \( 1.84 \)
- \( \sqrt{5} \approx 2.236 \)
- \( 2.3 \)
- \( 2.5 \)

On the second number line (for Problem 22), place the values:
- \( -3.5 \)
- \( -3.1 \)
- \( -3.01 \)
- \( -2.95 \)
- \( -2.9 \)

Would you like me to help with more details on how to graph these, or do you have any questions?

### Related Questions:
1. How do you calculate square roots of non-perfect squares?
2. Can you explain the difference between decimals and fractions in ordering?
3. What happens if two numbers are very close, how do we compare them precisely?
4. How do negative numbers behave differently on a number line?
5. What are other methods for estimating square roots accurately?

### Tip:
When comparing square roots, approximate their decimal form to simplify ordering!

Order each set of numbers from least to greatest. Verify your answer by graphing on a number line. Problem 21: 1.84, √5, 5/2, 2.3, √3. Problem 22: -3.01, -2.95, -2.9, -3.1, -3.5

Learn how to order numbers, including square roots, fractions, and decimals. This problem includes examples like √5, 5/2, and √3, and involves verifying the solution by graphing on a number line. Suitable for middle school students in Grades 6-8.

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